## Math 6 Chapter 2 Lesson 8: Rule of brackets

## 1. Summary of theory Tóm

### 1.1. Rule of brackets

- When removing the brackets with a “-” in front, we must change the signs of all terms in the brackets: the “+” sign into the “-” sign and the “-” sign into the “+” sign.
- When the parentheses with the “+” sign in front are removed, the signs of the terms in reverse remain the same.

**Example 1: **Quick calculation

a) 324 + [112 + (112 + 324)]

b) (-257) – [(-257 + 156) – 56].

__Solution guide__

a) 324 + [112 + (112 + 324)]

= 324 + [112 – 112 – 324]

= 324 – 324

= 0

b) (-257) – [(-257 + 156) – 56]

= -257 – (-257 + 156) + 56

= -257 + 257 – 156 + 56

= -100

### 1.2. Algebra total.

Because subtraction can be expressed as addition (plus the opposite of subtraction), a sequence of operations that adds and subtracts whole numbers is called an algebraic sum.

– When writing an algebraic sum, for simplicity, after converting subtractions to addition (with the number of opposites), we can omit all signs of addition and brackets. Such as:

5 + (-3) – (-6) – (+7) = 5 + (-3) + (+6) + (-7) = 5 – 3 + 6 – 7.

– Thanks to the commutative and associative properties and the bracket rule, we have the following conclusions:

- In an algebraic sum, we can: Change the positions of the terms arbitrarily with their signs.

Such as:

a – b – c = -b + a – c = -b – c + a

97 – 150 – 47 = 97 – 47 – 150 = 50 – 150 = – 100.

- Put brackets to group the terms arbitrarily, noting that if the brackets are preceded by a “-” then all terms must be enclosed in brackets.

Such as:

a – b – c = (a – b) – c = a – ( b + c)

284 – 75 – 25 = 284 – (75 + 25) = 284 – 100 = 184.

**Attention: **Without fear of confusion, we may be able to say that the algebraic sum is the sum.

**Example 2:** Simple expression

a. x + 25 + (-17) + 63

b. (-75) – (p+20) + 95

__Solution guide__

a. x + 25 + (-17) + 63 = x + 71

b. (-75) – (p+20) + 95 = – p

## 2. Illustrated exercise

**Question 1: **Remove the parentheses and calculate:

a. (18 + 29) + (158 – 18 – 29)

b. (13 -135 +49) –(13 +49)

__Solution guide__

a. (18 + 29) + (158 – 18 – 29)

=158

b. (13 -135 +49) –(13 +49)

=-135

**Verse 2:** Calculate the value of the expressions: x + b + c, knowing:

a. x = -3, b = -4, c = 2

b. x = 0, b = 7, c = -8

__Solution guide__

a. x + b + c = (-3) + (-4) + 2 = (-7) + 2 = -5

b. x + b + c = 0 + 7 + (-8) = -1

**Question 3: **Total

a. (-24) + 6 + 10 + 24

b. 15 + 23 + (-25) + (-23)

__Solution guide__

a. (-24) + 6 + 10 + 24 = 16

b. 15 + 23 + (-25) + (-23) = -10

## 3. Practice

### 3.1. Essay exercises

**Tree 1:** Quickly calculate the following sums:

a) (5674-97) – 5674

b) (-1075) – (29 – 1075)

**Verse 2: **Calculate

a) (18 + 29) + (158 – 18 – 29)

b) (13 – 135 + 49) – (13 + 49)

c) (-24) + 6 + 10 + 24

d) 15 + 23 + (-25) + (-23)

### 3.2. Multiple choice exercises Bài

**Question 1:** Simplifying the expression x + 1982 + 172 + (-1982) – 162 we get the result:

A. x – 10

B. x + 10

C. 10

D. x

**Verse 2:** Sum (-43567 – 123) + 43567 equals:

A. -123

B. -124

C. -125

D. 87011

**Question 3: **The result of the calculation (-98) + 8 + 12 + 98 is:

A. 0

B. 4

C. 10

D. 20

**Question 4: **Select the correct answers:

A. (-7) + 1100 + (-13) + (-1100) = 20

B. (-7) + 1100 + (-13) + (-1100) = -20

C. (-7) + 1100 + (-13) + (-1100) = 30

D. (-7) + 1100 + (-13) + (-1100) = -10

**Question 5: **Simplifying the expression 235 + x – (65 + x) + x we get:

A. x + 170

B. 300 + x

C. 300 – x

D. 170 + 3x

## 4. Conclusion

Through this lesson, you should know the following:

- Stick to the parenthesis rule.
- Define algebraic sum.

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